Due to a general shift in manufacturing paradigm from mass production towards mass customization, reconfigurable automation technologies, such as robots, are required. However, current industrial robot solutions are notoriously difficult to program, leading to high changeover times when new products are introduced by manufacturers. In order to compete on global markets, the factories of tomorrow need complete production lines, including automation technologies that can effortlessly be reconfigured or repurposed, when the need arises. In this paper we present the concept of general, self-asserting robot skills for manufacturing. We show how a relatively small set of skills are derived from current factory worker instructions, and how these can be transferred to industrial mobile manipulators. General robot skills can not only be implemented on these robots, but also be intuitively concatenated to program the robots to perform a variety of tasks, through the use of simple task-level programming methods. We demonstrate various approaches to this, extensively tested with several people inexperienced in robotics. We validate our findings through several deployments of the complete robot system in running production facilities at an industrial partner. It follows from these experiments that the use of robot skills, and associated task-level programming framework, is a viable solution to introducing robots that can intuitively and on the fly be programmed to perform new tasks by factory workers.